。
She has lots of books.
Literal
She [topic-は] a-lot [genitive-の] books [object-を] [has-持っている].
The verb 持っている ('have, possess') is the resulting-state form of 持つ ('hold, take in hand, come to have'); plain 持つ describes the act of grasping, while 持っている describes the ongoing state of possession. So 本を持っている is 'be in possession of books,' essentially 'have books.' The ~ている stative use with 持つ is one of the standard examples taught alongside 知っている for showing how ~ている marks resulting state rather than progressive action. たくさんの with the connecting の is required when たくさん modifies a noun directly.